CS 1520 / CoE 1520: Programming Languages for Web Applications (Spring 2013)
Department of Computer Science, University of Pittsburgh
Assignment #1: Perl
Due: 11:59pm, Friday, February 15th, 2013
Released: February 1st, 2013
Goal
Gain familiarity with Per
CS 1520 / CoE 1520: Programming Languages for Web Applications (Spring 2013)
Department of Computer Science, University of Pittsburgh
Term Project: Pittsburgh Interactive Research Accounting System (piras)
Due: 11:59pm, Saturday, April 27th, 2013
Released
CS 1520 / CoE 1520: Programming Languages for Web Applications (Spring 2013)
Department of Computer Science, University of Pittsburgh
Assignment #3: Javascript
Due: 11:59pm, Friday, April 19th, 2013
Released: April 4th, 2013
Goal
Gain familiarity with Jav
Our Company specializes in direct marketing and sales. Our account manager's objective is to create mutually
beneficial relationships for both our client?s and their customers; we do this by focusing our efforts on a direct
relationship-based marketing ap
ADVANCED CALCULUS I FOR UNDERGRADUATE STUDENTS
(MATH 1530)
HOMEWORK NO. 3
INSTRUCTOR & TEACHING ASSISTANT: GEORGE SPARLING & CEZAR LUPU
Problem 1. Decide which of the following sets is compact. For those that are
not compact, explain why. Give some reason
Advanced Calculus,
Final Exam, 12/13/14
Name:
The best six questions will count, 20 points per question
Question 1
'Iiue/false: give your reasons.
c There is an uncountable subset of the reais without limit points.
0 [0,1] x [1, 2] is connected.
1. A nonu
Advanced Calculus, Exam 1, 10 /'14_/ 14
Name:
Show your work.
Twenty points per question.
The best ve questions will count.
Question 1
For each of the following statements, either prove or disprove it.
o A continuous bijection from one metric space to ano
Solutions Homework, MATH 414, Fall 2010
Chapter 1, 12:) (a) Suppose there is no s [b , b] S. Then b < b is
an upper bound for S contradicting the assumption b = l.u.b.S.
(b) No. For example consider S = 1 with l.u.b.S = 1.
(c) x a = cfw_q Q : q < a|cfw_q
Advanced Calculus, Exam 2, 11/21/14
Name:
Twenty points per question.
The best six questions will count.
Question 1
For n a fixed positive integer, put f (x) = xn , for any non-negative x.
Using appropriate Riemann sums, determine, with proof, the integra
ADVANCED CALCULUS I FOR UNDERGRADUATE STUDENTS
(MATH 1530)
HOMEWORK NO. 5
INSTRUCTOR & TEACHING ASSISTANT: GEORGE SPARLING & CEZAR LUPU
Problem 1. Let p be a real number, p 6= 1. Compute
1p + 2p + . . . + np
.
n
np+1
lim
Problem 2. Let f : [a, b] R be a n
ADVANCED CALCULUS I FOR UNDERGRADUATE STUDENTS
(MATH 1530)
HOMEWORK NO. 4
INSTRUCTOR & TEACHING ASSISTANT: GEORGE SPARLING & CEZAR LUPU
Problem 1. (i) Show that ex x + 1 for each x R, with equality if and only
if x = 0.
a1 + a2 + . . . + an
(ii) Let ak >
Background:
T he problem is what are the best specifications for tin cans? Assume that the cans
will be made from tin sold in rolls of 2 meter width and 10 meter length. In reality lots
of food/drinks companies choose tin cans as containers so they might
Math 1530 Midterm Exam
October 17, 2011
Name:
Instructions: No books or notes may be used during the exam. Attempt all problems, giving complete and clear explanations of your answers.
1. (5 points each) Each of the items below gives a metric space X and
Math 1530
Topics for the Midterm Exam
Denitions
Supremum and inmum
Norm
Euclidean norm
Metric
Open set
Closed set
Interior point
Boundary point
Limit point
Closure
Continuous function
Limit of a sequence
Upper and lower limits
Cauchy sequence
Complete met
Math 1530
Solutions to Homework 7
December 5, 2011
Chapter 7 Number 15
The function f must be constant on [0, ). Let > 0. By equicontinuity, there
is a > 0 such that for all x [0, 1] with x < and all n N we have
|fn (x) fn (0)| < .
Let x [0, ) be arbitrar
Math 1530
Solutions to Homework 6
November 21, 2011
Chapter 4 Number 6
First, assume f is continuous. Dene F : E R2 by F (t) = (t, f (t). Then F
is continuous, and E is compact, so F (E ) is compact. But F (E ) is the graph
of f .
For the converse, by way
Math 1530
Solutions to Homework 5
November 5, 2011
Chapter 3 Number 8
Since
an bn converges if and only if
an (bn ) converges, there is no loss
in assuming that (bn ) is decreasing. Since (bn ) is monotone and bounded, it
converges to some real number b.
Math 1530
Solutions to Homework 4
October 25, 2011
Chapter 3 Number 3
We rst show that sn < 2 for every n N, by induction. The case n = 1 is
clear. Let n N, and suppose that sn < 2. Then
sn+1 =
2+
sn <
2+
2 < 2,
so, by induction, sn < 2 for every n N.
We
Math 1530
Solutions to Homework 3
October 7, 2011
Chapter 2 Number 19
(a) Since A and B are closed, A = A and B = B , so
A B = A B = A B = .
(b) Let A and B be disjoint open sets. For any p A there is a neighborhood
N of p which is contained in A, and the
Math 1530
Solutions to Homework 2
September 26, 2011
Chapter 1 Number 8
Let F be any ordered eld, and let a F with a = 0. Then either a > 0 or
a > 0. Since the product of positive elements is positive, and a2 = (a)2 , it
follows that a2 > 0. In particular